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What Does It Mean When An Equation Has No Solution?

What does it mean when an equation has no solution?

Summary

  1. The equation "x+4 = x+2" is an example of problem with no solution, as normal as it may look!
  2. Trying to combine x-terms on one side of the equation will result in a false statement
  3. The equation "10+6x = 15+6x" also looks normal but has no solution
  4. Plugging values such as '2' and '6' into "10+6x = 15+6x" will give you false statements
  5. Solving "10+6x = 15+6x" for 'x' will also result in a false statement
  6. So a problem with no solution will be false no matter what value you plug in for the variable

Notes

    1. We're going to look at a few problems that have no solution
    2. The equation "x+4 = x+2" is an example of problem with no solution
    3. "x+4" does NOT equal "x+2", so this example problem has no solution!
    4. Here, 'x' is just a variable
    1. As normal as the equation "x+4 = x+2" looks, it has no solution
    1. This means we need to subtract 'x' from both sides of the equation
    2. Here, 'x' is just a variable
    1. As normal as the equation "x+4 = x+2" looks, it has no solution
    2. x+4-x = 4
    3. x+2-x = 2
    4. Here, 'x' is just a variable
    1. After subtracting 'x' from both sides, we ended up with "4=2"
    2. Here, 'x' is just a variable
    1. After subtracting 'x' from both sides, we ended up with "4=2", which is a false statement
    2. Here, 'x' is just a variable
    1. For our first "no solution" example, we ended up with the false statement: 4=2
    1. Try plugging values for 'x' into "x+4 = x+2", and you'll always end up with a false statement
    2. Here, 'x' is just a variable
    3. For our first "no solution" example, we ended up with the false statement: 4=2
    1. We're now going to look at our second "no solution" example
    2. The equation "10+6x = 15+6x" is an example of problem with no solution
    3. Again, 'x' is just a variable
    1. The equation "10+6x = 15+6x" is an example of problem with no solution
    2. Again, 'x' is just a variable
    1. The equation "10+6x = 15+6x" is an example of problem with no solution, as normal as it may look!
    2. Again, 'x' is just a variable
    1. Try plugging values for 'x' into "10+6x = 15+6x", you'll always end up with a false statement
    2. Again, 'x' is just a variable
    1. Try plugging values for 'x' into "10+6x = 15+6x", you'll always end up with a false statement
    2. Again, 'x' is just a variable
    1. Plug in '2' for 'x' in the equation "10+6x = 15+6x"
    2. 10+6x = 10+6•2 = 10+12 = 22
    3. 15+6x = 15+6•2 = 15+12 = 27
    4. 6•2 = 12
    5. Again, 'x' is just a variable
    1. Plugging '2' into "10+6x = 15+6x" gave us a false statement: 22=27
    2. Again, 'x' is just a variable
    1. Plug in '6' for 'x' in the equation "10+6x = 15+6x"
    2. 10+6x = 10+6•6 = 10+36 = 46
    3. 15+6x = 15+6•6 = 15+36 = 51
    4. 6•6 = 36
    5. Here, 'x' is just a variable
    1. Try plugging other values for 'x' into "10+6x = 15+6x", you'll always end up with a false statement
    1. This time, we're not plugging anything in for 'x', we're just solving for 'x' by getting all x-terms on one side
    2. Again, 'x' is just a variable
    1. This time, we're not plugging anything in for 'x', we're just solving for 'x' by getting all x-terms on one side
    2. Subtracting '6x' from both sides is a way of combining like terms
    3. Again, 'x' is just a variable
    1. The x-terms in "10+6x = 15+6x" cancel out when you subtract '6x'
    2. 10+6x-6x = 10
    3. 15+6x-6x = 15
    4. Again, 'x' is just a variable
    1. The x-terms in "10+6x = 15+6x" cancel out when you subtract '6x'
    2. 10+6x-6x = 10
    3. 15+6x-6x = 15
    4. Again, 'x' is just a variable
    1. Our second "no solution" example problem was: 10+6x = 15+6x
    1. Now that we've seen some examples, let's define "no solution"
    2. A false statement is when one side of an equation does not equal the other side
    1. A false statement is when one side of an equation does not equal the other side
    1. You will never get a true statement from plugging values into an equation with no solution
    2. A false statement is when one side of an equation does not equal the other side
    1. You will never get a true statement from plugging values into an equation with no solution